Tim had to paint some boxes. On the first day, the number of boxes he painted was 10% of the number of boxes that he had not painted. One week later, he painted another 209 boxes. As a result, the total number of painted boxes became 13 more than ³₅ of the total number of boxes. How many more boxes were unpainted than painted on the first day?

	Painted	Not painted	Total
Before	1x5 = 5 u	10x5 = 50 u	11x5 = 55 u
Change	+ 209	- 209
After	5 u + 209	50 u - 209	55 u
Comparing painted and not painted boxes in the end	3x11 + 13 = 33 u + 13	2x11 - 13 = 22 u - 13	5x11 = 55 u

10% = ¹⁰₁₀₀ = ¹₁₀
Painted : Not painted = 1 : 10

The total number of boxes remains unchanged. Make the total number of boxes at first and in the end the same.  LCM of 11 and 5 is 55.

The number of boxes painted in the end is repeated.

33 u + 13 = 5 u + 209
33 u - 5 u = 209 - 13
28 u = 196

1 u = 196 ÷ 28 = 7

Number of more boxes that were not painted than painted on the first day
= 50 u - 5 u
= 45 u
= 45 x 7
= 315

Answer(s): 315